Question

Simplify the following:
$2\frac{3}{7} + \frac{11}{35} - 3\frac{13}{15}$

• A. $1\frac{13}{105}$
• B. $-1\frac{13}{105}$
• C. $-\frac{13}{105}$
• D. $\frac{13}{105}$

Answer 1

Answer:

$-1\frac{13}{105}$

1: Convert the mixed fractions to improper fractions

• $2\frac{3}{7} = \frac{(2 \times 7) + 3}{7} = \frac{17}{7}$

• $3\frac{13}{15} = \frac{(3 \times 15) + 13}{15} = \frac{58}{15}$

The expression becomes:
$\frac{17}{7} + \frac{11}{35} - \frac{58}{15}$

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2: Find a Lowest Common Denominator (LCM)

Find the LCM of the denominators 7, 35, and 15:

• Factors of 7: $7$

• Factors of 35: $5 \times 7$

• Factors of 15: $3 \times 5$

• $\text{LCM} = 3 \times 5 \times 7 = \mathbf{105}$

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3: Convert the fractions

Multiply the numerator and denominator of each fraction to reach the common denominator of 105:

• $\frac{17}{7} = \frac{17 \times 15}{7 \times 15} = \frac{255}{105}$

• $\frac{11}{35} = \frac{11 \times 3}{35 \times 3} = \frac{33}{105}$

• $\frac{58}{15} = \frac{58 \times 7}{15 \times 7} = \frac{406}{105}$

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4: Combine the terms

$\frac{255 + 33 - 406}{105}$
$= \frac{288 - 406}{105}$
$= -\frac{118}{105}$

Converting back to a mixed fraction:
$-\frac{118}{105} = -1\frac{13}{105}$